I don't know about Cook County, but you might be able to search online for the FPDCC regulations.

I got kicked out of a DuPage preserve last year, and I went home and looked up the regulations online. I was so sure I was right about being able to fly that I took them back to the park and showed them to the cop! The Dupage regulations state that you can't take off or land by kite, glider, ultralight, airplane, etc., but they do not specifically state that you can't fly kites. After I showed the regulations to the officer, he agreed that he should not have asked me to leave. I think he was new and therefore didn't really know the regulations in detail. So, I think if you have the regulations on your side (and have a copy) and are polite, you might be able to keep flying.

Of course, all this assumes you aren't flying power kites big enough to take off or land!

I called FPDCC main office and talked to both police and permit departments. They both agreed that flying a kite is permissible as long you are not endangering a public. Although I was not very specific about what kind of kit I was going to fly. Is there a way to obtain a copy of rules and regulations inside a park?

You could look here.. I got to that site from a link on the FPDCC web site - under the "About" link, and then I chose "Code" which took me to another page (here) with a link to the site I've linked in my first link .

Didn't see anything in the second section / recreation chapter on kite flying. However, I don't have time to read the whole thing.